Josh Hart joked that he didn’t expect to “play 47 minutes or have a triple-double” Saturday night in his first game in a Knicks uniform, but contributing at both ends of the floor to a key win certainly represented a nice first step for the trade-deadline acquisition.

Former Villanova teammate Jalen Brunson dropped a game-high 38 points, while the hard-nosed Hart provided all of the advertised intangibles off the bench in 25 minutes, including the entire fourth quarter, to propel the Knicks to a 126-120 victory over the Jazz at the Garden.

All-Star forward Julius Randle finished with 31 points, RJ Barrett scored 17 of his 20 in the second half and Immanuel Quickley added 15 points off the bench as the Knicks shook off their loss Friday in Philadelphia and improved to 31-27 entering a home matchup Monday against the gutted Nets.

In the first home game after acquiring Hart in a trade Wednesday night with the Trail Blazers, the Garden had an unmistakable heartbeat from the start.

The 27-year-old Hart replaced second-year guard Miles McBride in coach Tom Thibodeau’s nine-man rotation. Hart also played ahead of Quentin Grimes for all of the final period. He did a bit of everything to finish with 11 points, eight rebounds (four offensive), four assists and four steals.

“I just think all-around, the competitive spirit, his toughness, his rebounding, his playmaking ability, he does things that make your team better,” Thibodeau said before the game. “And so, that’s what I’m looking forward to. I know from having coached against him how I felt when he was on the floor.

“He makes hustle plays all the time, and those are the types of things that unite and inspire your team, too, because you can go on runs from that.”

First-time All-Star Lauri Markkanen scored 29 points and Jordan Clarkson had 24 for the Jazz (28-30).

Hart received a loud ovation when he checked in, along with Quickley and Isaiah Hartenstein, with 2:54 remaining in the first quarter. Hart drew a foul on a drive to the basket on his first offensive possession with the team. He sank one free throw and then collected a long feed from Brunson for a layup to draw more cheers.

One game after scoring 20 of his 30 points in the first quarter Friday in the loss to the 76ers, Brunson totaled 15 points in the opening 12 minutes on 6-for-8 shooting. Randle chipped in nine points for a 33-28 Knicks lead through the first quarter.

Hart’s strong play at both ends was exemplified when he picked off Walker Kessler’s pass and found Obi Toppin for a cutting bucket with a crisp bounce pass to give the Knicks an 11-point cushion nearly five minutes into the second quarter. But Hart drew three fouls in his opening nine-minute stint, and Grimes came back off the bench to replace him midway through the period.

A converted three-point play by Randle and Quickley’s corner trey pushed the lead to 12 with 2:21 remaining in the second before the Jazz drew back within six, 62-56, at intermission.

Markkanen and Collin Sexton combined for nine points in a 10-2 Utah run to open the second half for a 66-64 turnaround lead. But Barrett came alive after netting just three points in the first two quarters by nailing a 3-pointer and scoring again on a drive to the hoop as the Knicks rebuilt a five-point cushion.

Hart ran down two offensive rebounds on one possession later in the quarter, leading to a Randle tip shot that helped the Knicks carry an 87-84 lead into the final quarter.

Markkanen’s two 3-pointers in the opening five minutes of the fourth quarter evened the score, but Hart buried a 3-pointer from the corner off Brunson’s feed to put the Knicks up 104-101 with 6:44 remaining.

After Brunson connected from beyond the arc, another offensive board by Hart led to Barrett’s corner 3-pointer for a six-point bulge with 3:46 to play. Hart drew another huge roar from the crowd and banged his chest after swishing his second 3-pointer for a 123-114 advantage with 1:42 left.